Question

At what rate percent per annum will be the simple interest on a sum of money be (7/15) of the amount in 10 years.
1. 9%
2. 8%
3. 5%
4. 6%

Answer 1

Correct Answer - Option 1 : 9%

Given

Simple interest = (7/15) × Amount

Formula used

Amount = P + SI

Simple interest = (p × r × t)/100

Where p, r and t are principal, rate and time respectively

Calculation

Amount = p + [(p × r × t)/100]

⇒ Amount = p + [(p × r × 10)/100]

⇒ Amount = p + (pr/10)

⇒ Amount = (10P + Pr)/10

Simple interest = (p × r × 10)/100

⇒ Simple interest = (pr/10)

And simple interest = (7/15) × amount

Simple interest = (7/15) × [(10p + pr)/10]

⇒ pr/10 = 70p/150 + 7pr/150

⇒ pr/10 - 7pr/150 = 70p/150

⇒ (15pr - 7pr)/150 = 70p/150

⇒ 8pr/150 = 70p/150

⇒ r = 70/8

⇒ r = 8.85%

⇒ r = 9%

∴ Rate of interest is 9%